{
  "abstract": "The scalability of variational quantum algorithms is fundamentally limited by the barren plateau effect, where the cost-function variance vanishes with system size, rendering optimization impractical. Recent Lie-algebraic approaches for deep parameterized have enabled a unified analytical understanding of this challenge but require either the initial state or the measurement observable to belong to the dynamical Lie algebra generated by the circuit. Here, we introduce a representation-theoretic framework under $2$-design hypothesis showing that variational quantum landscapes admit a natural decomposition into irreducible representation channels. This yields exact expressions and analytical bounds for the cost-function variance applicable to arbitrary initial states and observables, with previous Lie-algebraic results emerging as a special case. We illustrate the framework by analyzing the energy landscape of the one-dimensional ANNNI model for several circuit architectures, revealing trainability regimes inaccessible to existing methods. Our results establish a general representation-theoretic framework for analyzing variational quantum landscapes, substantially extending the analytical theory of barren plateaus.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.04462",
  "author_total": 3,
  "authors": [
    {
      "name": "Pedro Alcântara"
    },
    {
      "name": "Leandro Morais"
    },
    {
      "name": "Rafael Chaves"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dj7vzsa3000aj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.04462",
  "fulltext_url": null,
  "id": "dj7vzsa3000aj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.04462",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7211919939",
  "pdf_url": "https://arxiv.org/pdf/2609.04462",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dj7vzsa3000aj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:14Z",
      "native_id": "2609.04462",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.04462"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "A Representation-Theoretic Framework for Characterizing Barren Plateaus",
  "title_text": "A Representation-Theoretic Framework for Characterizing Barren Plateaus",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:14Z",
  "url": "https://research.draconitic.com/paper/dj7vzsa3000aj",
  "venue": "arXiv",
  "versions": []
}